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Symmetric Multivariate And Related Distributions
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Book Synopsis Symmetric Multivariate and Related Distributions by : Kai-Tang Fang
Download or read book Symmetric Multivariate and Related Distributions written by Kai-Tang Fang and published by Springer. This book was released on 2013-08-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the joint effort of three authors, located thousands of miles apart from one another, and its preparation was greatly facilitated by modern communication technology. lt may serve as an additional example of international co-operation among statisticians specializing in statistical distribution theory. In essence we have attempted to amass and digest widely scattered information on multivariate symmetric distributions which has appeared in the Iiterature during the last two decades. Introductory remarks at the beginning of each chapter summarize its content and clarify the importance and applicability of the distributions discussed in these chapters; it seems unnecessary, therefore, to dwell in this Preface on the content of the volume. It should be noted that this work was initiated by the first author, who provided continuous impetus to the project, and a great many of tbe results presented in tbe book stem from bis own researcb or tbe research of bis associates and students during the last 15 years.
Book Synopsis Symmetric Multivariate and Related Distributions by : Kai Wang Fang
Download or read book Symmetric Multivariate and Related Distributions written by Kai Wang Fang and published by CRC Press. This book was released on 2018-01-18 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.
Book Synopsis Symmetric Multivariate and Related Distributions by : Kai Wang Fang
Download or read book Symmetric Multivariate and Related Distributions written by Kai Wang Fang and published by CRC Press. This book was released on 2018-01-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.
Book Synopsis Multivariate Analysis and Its Applications by : Theodore Wilbur Anderson
Download or read book Multivariate Analysis and Its Applications written by Theodore Wilbur Anderson and published by IMS. This book was released on 1994 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probability Inequalities in Multivariate Distributions by : Y. L. Tong
Download or read book Probability Inequalities in Multivariate Distributions written by Y. L. Tong and published by Academic Press. This book was released on 2014-07-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.
Book Synopsis Contemporary Experimental Design, Multivariate Analysis and Data Mining by : Jianqing Fan
Download or read book Contemporary Experimental Design, Multivariate Analysis and Data Mining written by Jianqing Fan and published by Springer Nature. This book was released on 2020-05-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection and analysis of data play an important role in many fields of science and technology, such as computational biology, quantitative finance, information engineering, machine learning, neuroscience, medicine, and the social sciences. Especially in the era of big data, researchers can easily collect data characterised by massive dimensions and complexity. In celebration of Professor Kai-Tai Fang’s 80th birthday, we present this book, which furthers new and exciting developments in modern statistical theories, methods and applications. The book features four review papers on Professor Fang’s numerous contributions to the fields of experimental design, multivariate analysis, data mining and education. It also contains twenty research articles contributed by prominent and active figures in their fields. The articles cover a wide range of important topics such as experimental design, multivariate analysis, data mining, hypothesis testing and statistical models.
Book Synopsis Symmetric and Asymmetric Distributions by : Emilio Gómez Déniz
Download or read book Symmetric and Asymmetric Distributions written by Emilio Gómez Déniz and published by MDPI. This book was released on 2021-01-21 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results.
Book Synopsis Multivariate T-Distributions and Their Applications by : Samuel Kotz
Download or read book Multivariate T-Distributions and Their Applications written by Samuel Kotz and published by Cambridge University Press. This book was released on 2004-02-16 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
Book Synopsis Continuous Multivariate Distributions, Volume 1 by : Samuel Kotz
Download or read book Continuous Multivariate Distributions, Volume 1 written by Samuel Kotz and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.
Book Synopsis The Laplace Distribution and Generalizations by : Samuel Kotz
Download or read book The Laplace Distribution and Generalizations written by Samuel Kotz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.
Book Synopsis Multivariate, Multilinear and Mixed Linear Models by : Katarzyna Filipiak
Download or read book Multivariate, Multilinear and Mixed Linear Models written by Katarzyna Filipiak and published by Springer Nature. This book was released on 2021-10-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Będlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.
Book Synopsis Robust Multivariate Analysis by : David J. Olive
Download or read book Robust Multivariate Analysis written by David J. Olive and published by Springer. This book was released on 2017-11-28 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents methods that are robust to the assumption of a multivariate normal distribution or methods that are robust to certain types of outliers. Instead of using exact theory based on the multivariate normal distribution, the simpler and more applicable large sample theory is given. The text develops among the first practical robust regression and robust multivariate location and dispersion estimators backed by theory. The robust techniques are illustrated for methods such as principal component analysis, canonical correlation analysis, and factor analysis. A simple way to bootstrap confidence regions is also provided. Much of the research on robust multivariate analysis in this book is being published for the first time. The text is suitable for a first course in Multivariate Statistical Analysis or a first course in Robust Statistics. This graduate text is also useful for people who are familiar with the traditional multivariate topics, but want to know more about handling data sets with outliers. Many R programs and R data sets are available on the author’s website.
Book Synopsis Multivariate Statistical Analysis by : Narayan C. Giri
Download or read book Multivariate Statistical Analysis written by Narayan C. Giri and published by CRC Press. This book was released on 2003-11-14 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, Multivariate Statistical Analysis, Second Edition addresses several added topics related to the properties and characterization of symmetric distributions, elliptically symmetric multivariate distributions, singular symmetric distributions, estimation of covariance matrices, tests of mean against one-sided alternatives, and correlations in symmetrical distributions. Its discussions and examples draw on a wide range of multivariate data, from biometry, agriculture, biomedical science, economics, to filtering and stochastic control, stock market data analysis, and random signal processing.
Book Synopsis Continuous Multivariate Distributions, Volume 1 by : Samuel Kotz
Download or read book Continuous Multivariate Distributions, Volume 1 written by Samuel Kotz and published by John Wiley & Sons. This book was released on 2019-01-17 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seit dem Erscheinen der ersten Auflage dieses Werkes (1972) hat sich das Gebiet der kontinuierlichen multivariaten Verteilungen rasch weiterentwickelt. Moderne Anwendungsfelder sind die Erforschung von Hochwasser, Erdbeben, Regenfällen und Stürmen. Entsprechend wurde das Buch überarbeitet und erweitert: Nunmehr zwei Bände beschreiben eine Vielzahl multivariater Verteilungsmodelle anhand zahlreicher Beispiele. (05/00)
Book Synopsis Copulae and Multivariate Probability Distributions in Finance by : Alexandra Dias
Download or read book Copulae and Multivariate Probability Distributions in Finance written by Alexandra Dias and published by Routledge. This book was released on 2013-08-21 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.
Book Synopsis Multivariate Statistical Methods by : György Terdik
Download or read book Multivariate Statistical Methods written by György Terdik and published by Springer Nature. This book was released on 2021-10-26 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a general method for deriving higher-order statistics of multivariate distributions with simple algorithms that allow for actual calculations. Multivariate nonlinear statistical models require the study of higher-order moments and cumulants. The main tool used for the definitions is the tensor derivative, leading to several useful expressions concerning Hermite polynomials, moments, cumulants, skewness, and kurtosis. A general test of multivariate skewness and kurtosis is obtained from this treatment. Exercises are provided for each chapter to help the readers understand the methods. Lastly, the book includes a comprehensive list of references, equipping readers to explore further on their own.
Book Synopsis Growth Curve Models and Statistical Diagnostics by : Jian-Xin Pan
Download or read book Growth Curve Models and Statistical Diagnostics written by Jian-Xin Pan and published by Springer Science & Business Media. This book was released on 2002-08-21 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. Provided are complete proofs of theorems as well as practical data sets and MATLAB code.
